(1) Field of the Invention
The present invention relates generally to determining wave propagation parameters and, more particularly, to determining wave propagation parameters of two dissimilar wave types that have been blended together.
(2) Description of the Prior Art
Measuring the wave propagation parameters of structures is important because these parameters significantly contribute to the static and dynamic response of the structures. Because most measurement methods are designed to isolate and measure one specific wave, they fail to correctly analyze dual wave propagation.
Resonant techniques have been used to identify and measure longitudinal properties for many years. These methods are based on comparing the measured eigenvalues of a structure to predicted eigenvalues from a model of the same structure. Resonant techniques only allow measurements at natural frequencies and do not have the ability to separate two different wave types propagating in a structure.
Comparison of analytical models to measured frequency response functions is another method that has been used to estimate stiffness and loss parameters of a structure. When the analytical model agrees with one or more frequency response functions, the parameters used to calculate the analytical model are considered accurate. If the analytical model is formulated using a numerical method, a comparison of the model to the data can be difficult due to dispersion properties of the materials. Additionally, many finite element algorithms have difficulty calculating responses of structures when there is a large mismatch in wavespeeds.
Previous efforts to solve problems related to the above are described by the following patents:
U.S. Pat. No. 4,321,981 issued Mar. 30, 1982, to K. H. Waters, discloses combination of fixed geometry of vibrating masses on a baseplate coupled to the ground, the masses being at a fixed angle to each other and of relatively variable phase, can be controlled to produce both compressional and shear waves simultaneously in a seismic exploration system.
U.S. Pat. No. 4,907,670, issued Mar. 13, 1990, to N. A. Anstey, discloses a method of seismic exploration using swept-frequency signals, compressional and shear waves are emitted simultaneously. Typically the waves are generated by swinging-weight vibrators acting through a single baseplate. If the frequency of the shear vibration is one-half that of the compressional vibration, the downward vertical forces can be phased to minimize the horizontal slippage of the baseplate. The sensitive axis of the geophones is inclined to the vertical for detecting both compressional waves and shear waves. For defined ranges of sweep rate, separate compressional and shear records are obtained by cross-correlating the geophone signal separately against the vertical and horizontal emissions.
U.S. Pat. No. 5,363,701, issued Nov. 15, 1994, to Lee et al., discloses a plurality of elongated test specimens undergo vibrations induced by ran noise within an acoustical frequency range establishing standing waves therein having resonant frequencies at which the collection of measurement data through accelerometers mounted at the ends of the specimens provides for calculation of physical material properties. The processing of the data during collection, analysis and calculation is automated by programmed computer control.
U.S. Pat. No. 5,533,399, issued Jul. 9, 1996, to Gibson et al., discloses a method and apparatus for deriving four independent elastic constants (longitudinal and transverse. Young's moduli, in-plane shear modulus and major Poisson's ratio) of composite materials from the modal resonance data of a freely-supported rectangular thin plate made from the material. The method includes the steps of: suspending a panel of the material from a rigid support by a plurality of filaments having a low support stiffness which has minimal effect on motion of the panel; providing a vibration sensor to detect a vibration response in the panel; imparting an impulse to the panel; generating a response signal proportionate to the response in the panel to the impulse imparted; generating an excitation signal in proportion to the impulse; communicating the signals to an analyzer for transforming the signals into a frequency domain; deriving resonance frequencies and associated mode shape indices of the panel; communicating the resonance frequencies and the mode shape indices to a computing device; and predicting and displaying the elastic constants using the computing device.
U.S. Pat. No. 5,663,501, issued Sep. 2, 1997, to Nakamura et al., discloses a vibration sensor is placed on each of the top surface of a layer of the structure and the ground surface near the structure so as to record vibrations. A seismic vulnerability data processor assumes a transfer function of vibration of the top surface of the layer of the structure based on a spectral ratio between the vibration recorded on the top surface of the layer of the structure and the vibration recorded on the ground surface, thereby obtaining a predominant frequency and amplification factor of vibration of the top surface of the layer of the structure. A seismic vulnerability index of the layer of the structure resulting from a deformation of the layer is obtained based on the obtained predominant frequency and amplification factor of vibration of the top surface of the layer of the structure and on the height of the layer of the structure. This seismic vulnerability index is multiplied by an assumed seismic acceleration so as to obtain a maximum shear strain of the layer of the structure upon being subjected to an earthquake.
U.S. Pat. No. 6,006,163, issued Dec. 21, 1999, to Lichtenwalner et al., discloses a An active damage interrogation (ADI) system (and method) which utilizes an array of piezoelectric transducers attached to or embedded within the structure for both actuation and sensing. The ADI system actively interrogates the structure through broadband excitation of the transducers. The transducer (sensor) signals are digitized and the transfer function of each actuator/sensor pair is computed. The ADI system compares the computed transfer function magnitude and phase spectrum for each actuator/sensor pair to a baseline transfer function for that actuator/sensor pair which is computed by averaging several sets of data obtained with the structure in an undamaged state. The difference between the current transfer function and the baseline transfer function for each actuator/sensor pair is normalized by the standard deviation associated with that baseline transfer function. The transfer function deviation for each actuator/sensor pair is then represented in terms of the number of standard deviations, or sigmas, from the baseline. This statistic, termed the TF Delta, is then processed by a windowed local averaging function in order to reduce minor variations due to random noise, etc. The Windowed TF Delta for each actuator/sensor pair is then integrated over the entire excitation frequency spectrum, to thereby produce the Cumulative Average Delta, which provides a single metric for assessing the magnitude of change (deviation from baseline) of that particular actuator/sensor transfer function. The Cumulative Average Delta (CAD) for each actuator/sensor transfer function provides key, first-level information which is required for detecting, localizing, and quantitatively assessing damage to the structure.
U.S. Pat. No. 6,205,859 B1, issued Mar. 27, 2001, to Kwun et al., discloses an improved method for defect detection with systems using magnetostrictive sensor techniques. The improved method involves exciting the magnetostrictive sensor transmitter by using a relatively broadband signal instead of a narrow band signal typically employed in existing procedures in order to avoid signal dispersion effects. The signal detected by the magnetostrictive sensor receiver is amplified with an equally broadband signal amplifier. The amplified signal is transformed using a time-frequency transformation technique such as a short-time Fourier transform. Finally, the signal characteristics associated with defects and anomalies of interest are distinguished from extraneous signal components associated with known wave propagation characteristics. The process of distinguishing defects is accomplished by identifying patterns in the transformed data that are specifically oriented with respect to the frequency axis for the plotted signal data. These identified patterns correspond to signals from either defects or from known geometric features in the pipe such as welds or junctions. The method takes advantage of a priori knowledge of detected signal characteristics associated with other wave modes (such as flexural waves) and sensor excitation as well the effects caused by liquid induced dispersion.
U.S. Pat. No. 4,418,573, issued Dec. 6, 1983, to Madigosky et al., discloses a fast and reliable method is disclosed for measuring the dynamic mechanical properties of a material, particularly its modulus of elasticity and loss factor. By this method the acoustic characteristics of a material can be determined. An elongate strip of material, whose properties are desired to be known, is provided with miniature accelerometers fixedly secured to its opposite ends. One end of the strip is excited by a random noise source which travels toward the other end where that end and accelerometer is allowed to move freely (unrestrained). The accelerometers measure the ratios of acceleration at two locations over an extended frequency range of 0.2 Hz to 25 KHz, and the information is processed through a fast Fourier transform spectrum analyzer for determining amplitude of acceleration ratio and phase difference between the two accelerometers from which Young's modulus and loss factor for that material are determined.
The above listed patents and other prior art do not provide for a method for estimating wave propagation parameters of two dissimilar wave type that have been blended together. More specifically the above listed prior art does not disclose methods for determining system response to different types of wave motion (e.g. compressional and shear wave motion) characterized using wave numbers, wavespeeds, and wave propagation coefficients which are determined/estimated based on measurements at various positions in the media using suitable sensors, e.g., accelerometers. Suitable measurements might comprise one or more measurements of strain, velocity, acceleration, or displacement.
Consequently, those skilled in the art will appreciate the present invention that addresses the above and other problems.